Linear Algebra (2500001) – Course 2025/26 PDF
Syllabus
Learning Objectives
Knowledge of vector spaces; Matrices; Determinants; Linear equation systems; Linear applications; Euclidean spaces; Reduction of endomorphisms and matrices; and symmetric and orthogonal operators. 1 Ability to interpret vector spaces. 2 Ability to solve linear equations systems both manually and through some basic computer program. 3 Ability to produce geometric interpretations of concepts in vector calculus. Knowledge of linear algebra, methods of solving linear problems that appear in engineering, elements of analytical geometry. Capacity for solving the mathematical problems posed in engineering involving these concepts. Knowledge of vector spaces. Knowledge of systems of linear equations, basic algorithms for the solution. Knowledge of analytical geometry. Knowledge of linear operators: endomorphisms and spectral theorems, related Euclidean spaces, eigenvalues and eigenvectors. Knowledge of determinants and their applications, particularly in the calculation of areas and volumes.
Competencies
Especific
Ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge about: linear algebra; geometry; differential geometry; differential and integral calculation; differential equations and partial derivatives; numerical methods; numerical algorithmic; Statistics and optimization. (Basic training module)
Total hours of student work
| Hours | Percentage | |||
|---|---|---|---|---|
| Supervised Learning | Large group | 20h | 33.33 % | |
| Medium group | 30h | 50.00 % | ||
| Laboratory classes | 10h | 16.67 % | ||
| Self Study | 90h | |||
Teaching Methodology
The course consists of 4 hours per week of classroom activity (large size group) and optionally 2 hours weekly for a workshop (medium size group). The 2 hours in the large size groups are devoted to theoretical lectures, in which the teacher presents the basic concepts and topics of the subject, shows examples and solves exercises. Another 2 hours in the large size groups is devoted to solving practical problems with greater interaction with the students. The objective of these practical exercises is to consolidate the general and specific learning objectives. In the 2 hours of workshop (medium size group), the students receive academic support to facilitate the understanding of the course. This support is materialized in two ways: (1) reminder of basic mathematical concepts which are essential to learn the new concepts introduced in the course; (2) guided problem solving of additional problems and tests from previous years. Support material in the form of a detailed teaching plan is provided using the virtual campus ATENEA: content, program of learning and assessment activities conducted and literature. Although most of the sessions will be given in the language indicated, sessions supported by other occasional guest experts may be held in other languages.
Grading Rules
The evaluation calendar and grading rules will be approved before the start of the course.
The final grade is obtained from partial qualifications as follows: E0: Continuous assessment activities E1: Test of the units developed on the first half of the academic term E2: Test of the units developed on the second half of the academic term E3: Global test of the course The student has to choose whether to take the test E2 or E3 NF1=0.3E0 + 0.35E1 + 0.35E2 NF2=0.3E0 + 0.7E3 Final Mark = max {NF1, NF2} The exams consist of a part with questions on concepts associated with learning objectives in terms of subject knowledge or understanding, application and a set of exercises Concerning to the grade E0, if there is the chance, some of the activities will be performed within the framework of the Engimath@UPC+ project. Criteria for re-evaluation qualification and eligibility: Students that failed the ordinary evaluation and have regularly attended all evaluation tests will have the opportunity of carrying out a re-evaluation test during the period specified in the academic calendar. Students who have already passed the test or were qualified as non-attending will not be admitted to the re-evaluation test. The maximum mark for the re-evaluation exam will be five over ten (5.0). The non-attendance of a student to the re-evaluation test, in the date specified will not grant access to further re-evaluation tests. Students unable to attend any of the continuous assessment tests due to certifiable force majeure will be ensured extraordinary evaluation periods. These tests must be authorized by the corresponding Head of Studies, at the request of the professor responsible for the course, and will be carried out within the corresponding academic period.
Test Rules
Failure to perform a laboratory or continuous assessment activity in the scheduled period will result in a mark of zero in that activity.
Office Hours
Napoleon Anento: make an appointment Xavier Marcote: make an appointment Javier Ozón: make an appointment
Bibliography
Basic
- Rojo, J. Álgebra lineal. 2a ed. Madrid: McGrawHill, 2007. ISBN 9788448156350.
- Rojo, J.; Martín, I. Ejercicios y problemas de álgebra lineal. 2a ed. Madrid: McGraw-Hill, 2004. ISBN 8448198581.
- Strang, G. Introduction to linear algebra. 6th ed. Wellesley, Mass.: Wellesley-Cambridge Press, 2023. ISBN 9781733146678.
Complementary
- Proskuriakov, I.V. 2000 problemas de álgebra lineal. Barcelona: Reverté, 1991. ISBN 9788429191264.
- Hoffman, K.; Kunze, R. Linear algebra. 2nd ed. India: Pearson, 2015. ISBN 9789332550070.